Friis User’s
Guide
Prof. C.W. Trueman
ECE Department
Concordia University
December 7, 2011
Program
FRIIS illustrates the Friis Transmission equation by drawing the antennas and
their radiation patterns on the computer screen, and then evaluating the Friis
Transmission Equation. This can be used
as a classroom demonstration and provides insight by showing the spatial
relationships of the antennas and their radiation patterns. Students can use the program to check their
answers to homework problems.
Click
this link to download the FRIIS program: Get FRIIS Program
The Friis Transmission Equation
The
transmitter “Tx” is located at
The
isotropic power density radiated by the Tx antenna is
The
power density at the receive antenna is
The effective area of the
receive antenna is
The power received into a
matched load is
Hence the Friis Transmission
Equation reads
Define the spatial loss
factor as
and write the Friis
Transmission Equation as
Divide both sides by 1
milliWatt and take logs to obtain
Expand
to obtain
Then
the received power in dBm or dB relative to one milliwatt is
where
the spatial loss and antenna gains in this equation are in dB.
The FRIIS Program
The
FRIIS program evaluates the Friis Transmission Equation in dB and shows the
spatial relationship of the antennas and their radiation patterns. To
illustrate the FRIIS program, consider the following problem. A 20 watt
transmitter operats at 147.06 MHz and has a gain of 4 dB. The receive antenna is 40 km away and has a
gain of 6 dB. Find the received
power. To solve this problem, run FRIIS
and enter information into the main menu.
The
menus use blue text strings, called “editable fields”, for entering numerical
values, and red text strings called “buttons” that you can click with the mouse
to obtain various actions.
Click
the mouse on the blue string giving the frequency value as 0.000 and the
editable field opens as shown above. Type 0.14706 to enter the frequency in GHz.
Note that the red “buttons” changed to
black; they are not active when you are entering text values. Type tab to move to the next blue text string
and enter the transmitted power of 20 watts. Type the “enter” key to return to
the menu; the buttons turn red to show that they are active.
Enter
the position of the transmitter as x=0,y=0 and the position of the receiver as
x=40,000,y=0 m. The problem says nothing
about the diretional patterns of the antennas so assume they are
omnidirectional in the plane of the screen. Click the red button “Specify the
transmitter radiation pattern”.
The
program offers an omnidirectional antenna, a half-wave dipole antenna, an
antenna with a cardioid pattern having a beamwidth of 180 degrees, and a
keyhole antenna pattern. A
keyhole pattern approximation has a specified forward gain over a specified
beamwidth. Outside the beamwidth of the
main beam, the gain is equal to the backward gain. For a narrow beamwidth the radiation pattern
resembles an old-fashioned keyhole.
For
the present problem click “Select an omnidirecdtional antenna”.
Click
on the blue “editable field” for the gain and enter “4”, then type the “enter” key
to make the “Return to the main menu” button active. Click the button to return
to the main menu. Similarly, set the receiver pattern to omnidirectional and
the gain to 6 dB, and return to the main menu.
Click
“Evalate the Friis Transmission Equation”.
The display shows the transmitter with an omni pattern drawn with the
radius proportional to the gain of 4 dB, and the receiver with a larger omni
pattern with a gain of 6 dB. The Tx
power is reported as 43 dBm and the gain as 4 dB. The distance is reported as 40,000 m and the
spatial loss as -107.84 dB. The receiver
gain is 6 dB, and the received power is reported as -54.83 dBm. The user can verify that these values satisfy
the Friis Transmission Equation.
From
the main menu, click “Tabulation of the link calculation” to obtain this
information screen. The right-hand
column evaluates the terms in the Friis Transmission Equation in decibels. Add up the transmitter power, the gain, the
spatial loss and the receiver gain to obtain the received power into a matched
load. Students can verify their values for the power density at the receiver
and for the effective area of the receive antenna.
This
problem illustrates the basic function of the program. The following examples illustrate other
radiation patterns and other configurations of antennas.
Directional Patterns
Consider the
following problem. A cell phone user at Tx communicates with a base station
antenna at Rx on top of a nearby building.
The transmit antenna at Tx behaves as a lossless, half-wave dipole
antenna oriented vertically, or in the z direction. The center of the antenna is 1.5 m above the
ground and the antenna is 100 m from the base of the building. The Rx antenna is omnidirectional and is
lossless. The center of the Rx antenna
lies in the plane of the face of the building at an elevation of 65 m above the
ground. The operating frequency is 1.9 GHz.
The transmitted power is 125 mW.
Enter the
information describing the problem into the main menu. Then click on “Specify the transmitter
radiation pattern” and choose the half-wave dipole pattern. Click on “Specify the receiver radiation
pattern” and choose the omnidirectional antenna, and set the gain to 0 dB.
Click on “Display
the Friis Transmission Equation” and the program shows a schmatic of the
problem, with the antenna pattern of the transmitter and the receiver, and calculates
the received power as -58.44 dBm. The transmit dipole is oriented vertically,
approximating the behavior of a cell phone held in the user’s hand against the
ear.
Base station
antennas are not omnidirectional. Select
the cardioid pattern for the base station antenna and change the rotation angle
to 225 degrees, so that the antenna approximately faces the transmitter. The 3
dB beamwidth of the cardioid pattern is 180 degrees. The cardiod pattern sends energy broadly in
the direction that the antenna is facing.
Orienting the pattern with a rotation angle of 225 degrees points the
beam towards the ground, where the cell phone users are located. The gain of the antenna is 3 dB; the received
power increases to -55.43 dBm.
If the user holds
the cell phone in a favorable position so that the dipole pattern points
approximately towards the base station, then the received power increases. Here the dipole pattern is oriented at 40
degrees, the Tx gain increases to about 2 dB and the received power to -53.48
dBm.
However,
if the user holds the handset in a very unfavorable position, the handset
antenna`s pattern may be oriented so that the minimum points approximately
towards the base station. In this
illustration, the handset’s gain drops to -13.08 degrees and the received power
to -68.59 dBm. The pattern can be
oriented so that the minimum points precisely towards the base station and then
no power is received!
Satellite Link Problem
A satellite in Low
Earth Orbit must communicate with a handheld satellite telephone. The operating frequency is 1.65 GHz and the
satellite is 780 km from the telephone.
The satellite transmits 14 watts and the transmit antenna has a gain of
6 dB. The receive antenna is a half-wave
dipole, and is oriented to point at the satellite. Find the received power.
For this problem,
put the receive antenna at x=0,y=0 and the transmit antenna at x=0,y=780,000
m. Model the satellite antenna as a
keyhole antenna with a gain of 6 dB, and set the Tx rotation angle to 270
degrees so the keyhole antenna pattern points down. The beamwidth and backward gain are
unimportant for this simple problem. Model the Rx antenna as a half-wave
dipole, with a rotation angle of 90 degrees. The figure shows the geometry and
the antenna patterns. It is seen that
the received power is -105 dBm.
A better choice for the receive antenna is a cardiod
pattern, that points up to the sky and has low field strengths toward the
ground. This also improves the signal to
noise ratio because the antenna does not receive as much noise power from the “warm”
ground and so its brightness temperature is reduced. We see that the gain of the cardoid of 3 dB
is about 1 dB more than the gain of the half-wave dipole, and the received
power increases to approximately -104 dBm.
Conclusion
The FRIIS program
illustrates the geometry of wireless links and relates the antenna patterns to
the location of the transmit and receive anetnnas. The program allows the user to explore the
effect of the pointing direction of the antennas on the received power. The program is useful for classroom
demonstrations and for students to verify answers to homework problems using
the Friis Transmission Equation.